MHB Does the Intermediate Value Theorem Apply If h(a) and h(b) Have Opposite Signs?

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I have a continuous function h(x) and the inequality h(b)<=0<=h(a). Can I apply IVT?
 
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Well, what are the hypotheses of the IVT? Are they satisfied in your case?
 
Ackbach said:
Well, what are the hypotheses of the IVT? Are they satisfied in your case?
Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.
 
TheDougheyMan said:
Isn't it just that h(x) is continuous and if u is a number between h(b) and h(a),
h(b) < u < h(a), then etc etc. I didn't think I could, but I just wanted to see a variation of it.

Exactly right. So you can conclude that there is a $c \in (a,b)$ (I'm assuming $a<b$) such that $h(c)=0$.
 
I posted this question on math-stackexchange but apparently I asked something stupid and I was downvoted. I still don't have an answer to my question so I hope someone in here can help me or at least explain me why I am asking something stupid. I started studying Complex Analysis and came upon the following theorem which is a direct consequence of the Cauchy-Goursat theorem: Let ##f:D\to\mathbb{C}## be an anlytic function over a simply connected region ##D##. If ##a## and ##z## are part of...
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